This invention relates in general to pulse generators, and, more particularly, to nonlinear transmission lines utilized in pulse compressors that are capable of generating large-amplitude, narrow-width pulses. Generation of picosecond pulses is necessary for many applications, including applications involving characterization of very high speed transient phenomena or very high bandwidth sampling, mixing, or speed/delay-time measurement. In these applications, the generated pulses can be used as a trigger, an excitation signal, or a time base reference.
Picosecond pulses are presently generated by several different techniques. One technique employs a "nonlinear transmission line."
A nonlinear transmission line is an LC ladder network, as shown in FIG. 1, in which the capacitance of capacitors C.sub.k is dependent on the voltage across them and/or the inductance of inductors L.sub.k is dependent on the current through them. In some instances, actual implementations of nonlinear transmission lines have been constructed using varactor diodes as the voltage-variable capacitors and either discrete lumped-element inductors or lengths of transmission line as the inductors.
The pulse-shaping characteristic of such a nonlinear transmission line is a result of the voltage-dependent and/or current-dependent time delay ##EQU1## where V.sub.k is the voltage across the k.sup.th varactor diode and I.sub.k is the current through the k.sup.th inductor. As an example, if L.sub.k is constant and C.sub.k (V.sub.k) decreases with increasing voltage, then a higher-voltage portion of an input signal in the form of a pulse will travel faster through this section of the nonlinear transmission line than a lower-voltage portion of the pulse. This results in a steepening of the leading edge of the pulse and a slowing of the trailing edge. A numerical simulation (SPICE) displaying this effect is shown in FIG. 2.
The considerations of transition-time limitations, the number of varactor cells necessary for a particular amount of pulse shaping, and impedance matching have been discussed and analyzed to varying degrees of sophistication by other workers to describe the properties of travelling waves on nonlinear transmission lines in constant impedance environments. See, for example, R. B. Riley, "An Analysis of a Nonlinear Transmission Line," PhD. Dissertation, Stanford University, 1961; M. Birk and Q. A. Kerns, "Varactor Transmission Lines," Engineering Note EE-922, Lawrence Radiation Laboratory, University of California, May 22, 1963; H. Nagashima and Y. Amagishi, "Experiment on Solitons in the Dissipative Toda Lattice Using Nonlinear Transmission Line," Journal of the Physical Society of Japan, vol. 47, pp. 2021-2027, December 1979; and M. J. W. Rodwell, D. M. Bloom, and B. A. Auld, "Nonlinear Transmission Line for Picosecond Pulse Compression and Broadband Phase Modulation," Electronics Letters, vol. 23, pp. 109-110, Jan. 29, 1987. However, these references do not address problems associated with varactor diode turn-on and punch-through voltage limitations, soliton compression and inefficient use of varactor diode nonlinearity, reflections from mismatched load and source impedances, and ringing and soliton generation when it is not desired.
Considered in more detail, as discussed by Lundien, et al., "Hyperabrupt Junction Varactor Diodes for Millimeter-Wavelength Harmonic Generators," IEEE Trans. Microwave Theory and Techniques, vol. MTT-31, pp. 235-238, February 1983, and references cited therein, a varactor diode, when utilized for its nonlinear properties, is ideally meant to be operated over a voltage range bounded by the punch-through voltage of the varactor diode (the maximum usable reverse-bias voltage) and the turn-on voltage of the varactor diode (the maximum usable forward-bias voltage). The punch-through voltage V.sub.deplete is the voltage at which there is not further change in varactor capacitance. It is assumed that the breakdown voltage is greater than or equal to V.sub.deplete.
These constraints are equally true for varactor diodes utilized in nonlinear transmission lines. Typically, known nonlinear transmission lines comprise a series of identical cells, each of which incorporates a single varactor diode having the same parametric values as the other varactor diodes in the other cells. Any portion of a pulse or step which exceeds V.sub.deplete of the varactor diode in a cell of a nonlinear transmission line will pass through that cell without being acted upon by the nonlinearity and therefore will be unchanged. This results in the inability to steepen or compress the entire step or pulse. Conversely, if the peak voltage of the propagating pulse or step is less than V.sub.deplete, then the full nonlinearity of the varactor diode is not utilized. This results in less steepening and compression per unit length of nonlinear transmission line. In general, the highest power transfer efficiency and greatest steepening and compression are achieved when neither the turn-on voltage nor the breakdown voltage is exceeded and the full nonlinearity of the varactor diode in each cell is utilized without exceeding the punch-through voltage. There are two general areas where these ideal goals are difficult to achieve when using a series of identical single-varactor cells in nonlinear transmission lines.
First, some applications use voltages which are simply beyond the capabilities of a single-varactor cell from a given realizable varactor diode fabrication process. Accordingly, it would be desirable to provide a nonlinear transmission line which is not limited to a given varactor diode fabrication process and which can accommodate pulses and steps which would otherwise turn on and/or greatly exceed the punch-through voltage of a series of identical single-varactor cells.
Second, Tan, et al., U.S. Pat. No. 4,855,696 discloses a unique nonperiodic cell structure for a nonlinear transmission line, which allows the propagation and compression of a single soliton. An interesting feature of the disclosed pulse compressor is the increase in amplitude of the soliton as it propagates from the input of the nonlinear transmission line to the output. This causes each varactor diode in the pulse compressor to experience a different voltage excursion. When using a single varactor per cell and all of the varactor diodes have the same punch-through voltage, it is necessary for optimum performance to choose varactor parameters such that V.sub.deplete is equal to the highest peak voltage V.sub.max of the soliton on the pulse compressor. If V.sub.max exceeds V.sub.deplete, the full-width-at-half-maximum (FWHM) of the output pulse is increased, the amount of uncompressed energy is increased, and the peak voltage amplitude is reduced when compared to the result if V.sub.max equals V.sub.deplete. Because of the desirability to have V.sub.max equal to V.sub.deplete, the full nonlinearity of the varactor diodes is not utilized in all the other cells where the peak voltage of the propagating soliton is much less than V.sub.deplete. Accordingly, it would be desirable to provide a nonlinear transmission line which utilizes a greater range of the nonlinearity of the varactor diode in each cell and therefore produces increased pulse or step compression for a given length of nonlinear transmission line.
Additionally, when using only identical single-varactor cells from a given varactor diode fabrication process, only a limited range of steepening parameters and source and load impedances can be accommodated. Within these constraints the power transfer through the nonlinear transmission line should be maximized. However, power reflected from significantly mismatched load and source impedances can re-enter the nonlinear transmission line, reducing the power transfer from input to output. This occurs for two reasons.
First, low impedance sources and loads will invert the polarity of reflections. The inverted reflection has the proper polarity to forward bias and turn on varactor diodes in the nonlinear transmission line. Second, high impedance sources and loads step up the voltage of reflections. This will generate voltages which can exceed the punch-through voltage of the varactor diodes in the nonlinear transmission line. In addition, depending on the position of the mismatch with respect to the nonlinear transmission line and the resulting timing of the reflection, the reflection (both noninverted and inverted) can actually pass all the way back through the nonlinear transmission line. Accordingly, it would be desirable to provide a nonlinear transmission line which optimizes power transfer by minimizing reflections due to source and load impedance mismatches.
Furthermore, both Hirota, et al., "Theoretical and Experimental Studies of Lattice Solitons in Nonlinear Lumped Networks," Proc. IEEE, vol. 61, pp. 1483-1491, October 1973, and Kolosick, et al., "Properties of Solitary Waves as Observed on a Nonlinear Dispersive Transmission Line," Proc. IEEE, vol. 62, pp. 578-581, May 1974, describe experiments in which various types of pulses and steps are input to a nonlinear transmission line. They demonstrate that input pulses and steps eventually break up into one or more solitons if allowed to propagate for a sufficient time along a nonlinear transmission line. Also, as stated by Jager in "Characteristics of travelling waves along the non-linear transmission lines for monolithic integrated circuits: a review," Int. J. Elect., vol. 58, p. 662, 1985, "Any arbitrary initial signal decomposes into a well-defined superposition (non-linear) of individual solitary waveforms . . . " This phenomenon is exhibited by the steepening of the pulse or step until the risetime reaches approximately 2/f.sub.c (f.sub.c is the cutoff frequency of the nonlinear transmission line), whereupon the greater dispersion forces the generation of oscillatory tails (or ringing) which then eventually decompose into solitons.
In applications where nonlinear transmission lines are used for edge sharpening (e.g., in samplers and step-generators) the generation of oscillatory tails is generally not welcome, since they can degrade circuit performance specifications related to flatness and stability. Accordingly, it would be desirable to provide a nonlinear transmission line in which ringing is suppressed without significantly affecting the overall risetime of the steepened edge.